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          软考-数据结构4
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        <h4 id="图-最小生成树"><a href="#图-最小生成树" class="headerlink" title="图 - 最小生成树"></a>图 - 最小生成树</h4><h5 id="相关名词"><a href="#相关名词" class="headerlink" title="相关名词"></a>相关名词</h5><ul>
<li><p><code>连通图</code>：在无向图中，若任意两个顶点<code>Vi</code>与<code>Vj</code>都有路径相通，则称该无向图为连通图。</p>
</li>
<li><p><code>强连通图</code>：在有向图中，若任意两个顶点<code>Vi</code>与<code>Vj</code>都有路径相通，则称该 <strong>有向图</strong> 为 <strong>强连通图</strong>。</p>
</li>
<li><p><code>连通网</code>：在连通图中，若图的边具有一定的意义，每一条边都对应着一个数，称为 <strong>权</strong>；权代表着连接两个顶点的代价，这种 <strong>连通图</strong> 被称为 <strong>连通网</strong>。</p>
</li>
<li><p><code>生成树</code>：一个连通网的生成树是指一个子连通网，它包含图中全部 n 个顶点，但只有足以构成一棵树的 <code>n - 1</code> 条边。</p>
<p>一棵有 n 个顶点的生成树有且仅有 <code>n - 1</code> 条边，如果生成树中再添加一条边，则必定成环。</p>
</li>
<li><p><code>最小生成树</code>：在连通网的所有生成树中，所有边的 <strong>代价和最小</strong> 的生成树，称为最小生成树。</p>
</li>
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<span id="more"></span>
<h5 id="最小生成树算法"><a href="#最小生成树算法" class="headerlink" title="最小生成树算法"></a>最小生成树算法</h5><h6 id="Kruskal算法"><a href="#Kruskal算法" class="headerlink" title="Kruskal算法"></a><code>Kruskal</code>算法</h6><p>它可以称为 <strong>“加边法”</strong>，初始最小生成树边数为 <strong>0</strong>， 每迭代一次就选择一条满足条件的最小代价边，加入在最小生成树的边集合里。</p>
<h6 id="Prim算法"><a href="#Prim算法" class="headerlink" title="Prim算法"></a><code>Prim</code>算法</h6><p>它可以称为 <strong>“加点法”</strong>，每次迭代选择代价最小的边对应的点，加入到最小生成树中。算法从某一顶点 <strong>s</strong> 开始，逐渐长大覆盖整个连通网的所有顶点。</p>
<h5 id="总结"><a href="#总结" class="headerlink" title="总结"></a>总结</h5><p>因为 <strong>Kruskal</strong> 涉及大量对边的操作，所以它适用于稀疏图；<strong>普通的Prim算法</strong>适用于稠密图，但对有堆优化的 <strong>Prim算法</strong> 更适用于稀疏图，因为其时间复杂度是由边的数量决定的。</p>

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